Conflict-Aware Fusion: Mitigating Logic Inertia in Large Language Models via Structured Cognitive Priors
Qiming Bao, Xiaoxuan Fu, Michael Witbrock
cs.AI
Dec 6, 2025 · v8
cs.CL cs.LG cs.LO
TL;DR
Translates logical reasoning questions into Lean 4 and uses the Lean kernel as a verification oracle for RL rewards, measuring kernel agreement.
Abstract
Large language models (LLMs) achieve high accuracy on many reasoning benchmarks but remain brittle under structural perturbations of rule-based systems. We introduce a diagnostic framework with four stress tests – redundant vs. essential rule deletion, contradictory-rule injection, logic-preserving rewrites, and multi-law stacking – and use it to expose Logic Inertia: the tendency of generative LLMs (Qwen2/3, TinyLlama, GPT-4o, Gemma-3-4B-IT) and the encoder-only BERT baseline to persist along learned deductive trajectories under inconsistent premises. The collapse is sharp: untreated baselines fall from accuracy 1.00 on the base task to 0.00 on contradiction injection (instance-level exact match), and GPT-4o resolves only 56.0% of contradiction cases. We propose Conflict-Aware Fusion, a four-stage training pipeline that enforces verification-before-deduction as a learned structural prior: (i) SFT establishes the verification preamble; (ii) DPO sharpens the halt-on-contradiction decision boundary; (iii) Logical Invariance REgularisation (LIRE) penalises divergence between logically equivalent rule formulations via symmetric KL; (iv) Reinforcement Learning from Verification Feedback (RLVF) uses a symbolic forward-chaining engine as a deterministic oracle reward, jointly optimising invariance and sensitivity. The pipeline saturates all four primary stress tests for both 1.5B and 8B backbones. We further validate a Phase 2 extension that replaces the propositional oracle with a Lean 4 kernel, attaining 99.0% kernel agreement on the 105 classically-derivable (T) questions within a stratified 187-question Lean-translated sample (overall 71.7% across both polarities), providing a sound upgrade path to formally verified RL training. Code and benchmark:
https://github.com/14H034160212/lemoProblem
LLMs reach high accuracy on rule-based reasoning benchmarks but break under structural perturbations. Contradictory-rule injection is the worst case: models keep following learned deductive trajectories, a failure the authors call Logic Inertia.
Approach
Four stress tests probe this: redundant vs. essential rule deletion, contradiction injection, logic-preserving rewrites, and multi-law stacking. The proposed Conflict-Aware Fusion pipeline combines SFT, DPO, a symmetric-KL invariance regulariser (LIRE), and RL from verification feedback (RLVF) using a symbolic forward-chaining oracle reward. A Phase 2 extension replaces the propositional oracle with a Lean 4 kernel applied to Lean-translated questions.
Results
Untreated baselines fall from 1.00 accuracy on the base task to 0.00 under contradiction injection, and GPT-4o resolves 56.0% of contradiction cases. The pipeline saturates all four stress tests for 1.5B and 8B backbones. The Lean 4 kernel agrees on 99.0% of the 105 classically derivable questions in a 187-question sample, and 71.7% overall.
